1.8: Chapter 1 Reference Guide- Coordinate Systems, Units, Terminology

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This reference guide covers some topics that are outlined in Roland Stull’s Practical Meteorology: An Algebra-based Survey of Atmospheric Science Chapter 1, which may be useful to you going forward. These topics include the following.

Meteorological Conventions

This section describes standard meteorological conventions that are necessary to keep in mind when solving problems in this course. It includes different coordinate systems, including Cartesian coordinates, polar coordinates, and spherical coordinates. You are likely already well acquainted with Cartesian coordinates, but polar and spherical coordinates may be new to you. The standard way of describing and plotting wind direction is also given here.

Cartesian coordinates: $x, y$, and $z$ and velocity: $u, v$, and $w$.

Polar coordinates: direction and magnitude.

Wind in Cartesian coordinates: $(U, V)$
Wind in Polar coordinates: $(\alpha, M)$

Algebraically, wind is given a magnitude (wind speed) and a direction. Wind direction is split up into different components. When only horizontal wind motion is taken into account, we use $U$ and $V$, and vertical air motions are denoted by $W$.

$U$-> Wind in the $x$-direction
$V$-> Wind in the $y$-direction
$W$-> Wind in the $z$-direction (vertical air motion)

Because of this, wind can be plotted using polar coordinates, wind direction (dir) and wind magnitude (spd).

Wind directions are given by angle, with 0° to the north, and degrees increasing clockwise. Winds are described using the direction from which they come. A westerly wind is a wind from the west. Hawaiʻi is often impacted by the easterly or northeasterly trade winds, which come from the east and northeast.

\[spd=\left(U^2+V^2\right)^{1 / 2} \nonumber \]

\[\operatorname{dir}=90-(360 / C) * \arctan \left(\frac{V}{U}\right)+0 \nonumber \]

Sometimes, cylindrical coordinates $(M, \alpha, W)$ are used which are similar to polar coordinates in that magnitude and direction of wind velocity are used, but also include the vertical motion component $W$.

The Stull text uses the words “ordinate” and “abscissa”. Ordinate is simply the vertical axis (typically the y-axis) and abscissa is the horizontal axis (typically the x-axis). Independent variables are usually plotted on the x-axis, with dependent variables plotted on the y-axis.

Earth Frameworks Reviewed

The Earth is not a sphere, but it is pretty close. The distance between the center of the Earth and the north and south poles differs by about 20 km, so the Earth is referred to as an oblate spheroid.

Cartography

Meridians, which are north-south lines on a globe, are given by degrees longitude. Think of the distance between the north and south poles as long.

The prime meridian lies at 0° longitude, and passes through Greenwich, Great Britain.
East of here (defined as the Eastern Hemisphere, 0 – 180 °E), longitude is positive.
West of the prime meridian (Western Hemisphere, 0 – 180 °W), longitude is negative.
The Earth rotates counterclockwise about its axis.

Parallels, which are east-west lines on a globe, are given by degrees latitude. A good way to remember this is “Lat” rhymes with “flat” — just like the east-west horizontal (flat) lines of latitude.

The Equator is 0° latitude, with latitudes north of the Equator as positive (Northern Hemisphere: 0 – 90°N), and latitudes south of the Equator are negative (Southern Hemisphere: 0 – -90°S).

A helpful approximation between degrees of latitude and distance is that each degree of latitude is approximately 111 km, or about 60 nautical miles.

Chapter 1: Questions to Consider

Drag and drop the correct labels to the appropriate layers of the atmosphere.

Query $\PageIndex{1}$

Mauna Kea on Hawaiʻi Island is 13,803 feet tall at the summit. If the pressure at sea level is 1015 hPa and the scale height is 8 km, what is the pressure at the summit? (Hint: don’t forget to check the units!)
The pressure at the ground floor of a high-rise building is 1012 hPa. On the roof the pressure is 1007 hPa. If you assume that the air density is 1.2 kg·m^-3 and acceleration due to gravity is -9.8 m·s^-2, approximately how tall is the building?
In this chapter you learned about two different equations that describe the change in air pressure (P) with altitude (z):

$\begin{align*} P(z)=P_0*exp(\frac{-z}{H}) \end{align*}$

$\begin{align*} and \end{align*}$

$\begin{align*} \Delta P = -\rho * g * \Delta z \end{align*}$

When is the exponential equation preferable? When is the hydrostatic equation preferable? In questions two and three above, which equation did you use, and would your answers change if you used the other instead? Think about the assumptions that go into each equation and which variables are assumed to remain constant while pressure varies.

Selected Practice Question Answers:

Query $\PageIndex{2}$

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Chapter 1: Questions to Consider